"on-axis null" in horn speakers?

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All wave fronts diffract from the mouth edge of a horn to a certain extent. The more abrupt this termination the more diffraction there is. Now, if the mouth of the horn is round then at some frequency and far field location the diffracted waves will be uniformly 180 degrees out of phase from he direct wave. This will cause cancellation. A round horn will be the worst case, followed by an elliptical one, because for the circular mouth the distance to the axis are all the same. You will almost never see this effect in a square mouth horn because the path lengths all differ. The width and depth of the cancellation depends on many factors that are far too complex to get into in a forum post.

Also, the wave front arriving at the mouth must be fairly coherent of the diffraction won't be coherent and the null will be diminished. Hence you will not tend to see this effect on any horn which has internal diffraction. they will have numerous peaks and dips and one could not really say what is an axial cancellation and what isn't.
 
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